Question
What is the quotient and remainder when $ 1043 $ is divided by $ 3 $ ?
Answer
The quotient is 347 and the remainder is 2.
Explanation
| Division Table | ||||
| 0 | 3 | 4 | 7 | |
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| – | 9 | |||
| 1 | 4 | |||
| – | 1 | 2 | ||
| 2 | 3 | |||
| – | 2 | 1 | ||
| 2 | ||||
|
STEP 0: set up a division table |
||||
| 3 | 1 | 0 | 4 | 3 |
|
STEP 1: DIVIDE 1 : 3 = 0 with a remainder of 1 |
||||
| 0 | ||||
| 3 | 1 | 0 | 4 | 3 |
|
STEP 2: MULTIPLY 0 · 3 = 0 |
||||
| 0 | ||||
| 3 | 1 | 0 | 4 | 3 |
| 0 | ||||
|
STEP 3: SUBTRACT 1 - 0 = 1 |
||||
| 0 | ||||
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | ||||
| STEP 4: BRING DOWN | ||||
| 0 | ||||
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
|
STEP 5: DIVIDE 10 : 3 = 3 with a remainder of 1 |
||||
| 0 | 3 | |||
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
|
STEP 6: MULTIPLY 3 · 3 = 9 |
||||
| 0 | 3 | |||
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| 9 | ||||
|
STEP 7: SUBTRACT 10 - 9 = 1 |
||||
| 0 | 3 | |||
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| – | 9 | |||
| 1 | ||||
| STEP 8: BRING DOWN | ||||
| 0 | 3 | |||
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| – | 9 | |||
| 1 | 4 | |||
|
STEP 9: DIVIDE 14 : 3 = 4 with a remainder of 2 |
||||
| 0 | 3 | 4 | ||
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| – | 9 | |||
| 1 | 4 | |||
|
STEP 10: MULTIPLY 4 · 3 = 12 |
||||
| 0 | 3 | 4 | ||
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| – | 9 | |||
| 1 | 4 | |||
| 1 | 2 | |||
|
STEP 11: SUBTRACT 14 - 12 = 2 |
||||
| 0 | 3 | 4 | ||
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| – | 9 | |||
| 1 | 4 | |||
| – | 1 | 2 | ||
| 2 | ||||
| STEP 12: BRING DOWN | ||||
| 0 | 3 | 4 | ||
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| – | 9 | |||
| 1 | 4 | |||
| – | 1 | 2 | ||
| 2 | 3 | |||
|
STEP 13: DIVIDE 23 : 3 = 7 with a remainder of 2 |
||||
| 0 | 3 | 4 | 7 | |
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| – | 9 | |||
| 1 | 4 | |||
| – | 1 | 2 | ||
| 2 | 3 | |||
|
STEP 14: MULTIPLY 7 · 3 = 21 |
||||
| 0 | 3 | 4 | 7 | |
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| – | 9 | |||
| 1 | 4 | |||
| – | 1 | 2 | ||
| 2 | 3 | |||
| 2 | 1 | |||
|
STEP 15: SUBTRACT 23 - 21 = 2 |
||||
| 0 | 3 | 4 | 7 | |
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| – | 9 | |||
| 1 | 4 | |||
| – | 1 | 2 | ||
| 2 | 3 | |||
| – | 2 | 1 | ||
| 2 | ||||
|
STEP 15: SUBTRACT 23 - 21 = 2 |
||||
| 0 | 3 | 4 | 7 | |
| 3 | 1 | 0 | 4 | 3 |
| – | 0 | |||
| 1 | 0 | |||
| – | 9 | |||
| 1 | 4 | |||
| – | 1 | 2 | ||
| 2 | 3 | |||
| – | 2 | 1 | ||
| 2 | ||||
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